How do I use a free body diagram in this case?

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Discussion Overview

The discussion revolves around the application of free-body diagrams to determine the acceleration of mass m1 in a system involving two masses, m1 and m2, under the influence of an external force F. Participants explore how to effectively use free-body diagrams in both horizontal and vertical contexts, considering the implications of frictionless surfaces.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant suggests that the acceleration a for m1 can be calculated by treating m1 and m2 as a system, leading to a = F/(m1+m2), and questions how to use a free-body diagram for the same purpose.
  • Another participant emphasizes that m2 only affects vertical motion and not horizontal acceleration, prompting a discussion about the role of the support arm and its rigidity.
  • A later reply confirms that the support arm is rigidly holding m2 in place and raises the question of whether m2 affects the acceleration of m1 while it is on top of m1.
  • One participant asserts that m2 does not affect the acceleration of m1 due to the absence of friction, indicating that the free-body diagram cannot be used to determine how much of the force F accelerates each mass.

Areas of Agreement / Disagreement

Participants express differing views on the influence of m2 on the acceleration of m1, particularly regarding the role of friction and the use of free-body diagrams. The discussion remains unresolved with multiple competing perspectives on how to approach the problem.

Contextual Notes

There are limitations related to the assumptions about the rigidity of the support arm and the frictionless nature of the surfaces, which affect the participants' reasoning about the system's dynamics.

EddiePhys
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In the above cases I want to find the acceleration a for m1. I can do it by considering m1 and m2 to be a system, which would give me a = F/(m1+m2). How can I use a free-body diagram instead to calculate the acceleration? Using a free-body diagram, m2 only affects the vertical motion by exerting a vertical force and not the horizontal acceleration but we know that since the mass of the system has increased the acceleration will decrease. TLDR; how would I solve for the acceleration of m1 in both of the above cases using only a free-body diagram. All surfaces are frictionless.
 
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EddiePhys said:
Using a free-body diagram, m2 only affects the vertical motion by exerting a vertical force and not the horizontal acceleration

In the first diagram, is the support arm holding m2 rigid, and rigidly attached to m1? It might make things more clear if you consider the support arm as a third object with a very small mass.

In the second diagram, if the contact between m1 and m2 is indeed frictionless, what should you expect to happen, intuitively, when you push on m1 (alone)? Have you ever pushed one object out from underneath another one that is resting on top of it?
 
jtbell said:
In the first diagram, is the support arm holding m2 rigid, and rigidly attached to m1? It might make things more clear if you consider the support arm as a third object with a very small mass.

In the second diagram, if the contact between m1 and m2 is indeed frictionless, what should you expect to happen, intuitively, when you push on m1 (alone)? Have you ever pushed one object out from underneath another one that is resting on top of it?

1) Yes, it's holding m2 in place
2) Yes, it would slide from beneath m2, but for the time m2 is on top of m1, wouldn't it affect the acceleration?

Could you please show me how to make a free-body diagram in the two cases such that the horizontal acceleration is affected too?
 
For 2) above, no it would not affect the acceleration of m1 because there is no friction so no force.

I'm not sure what you're getting at with your question. My best guess is you want to figure out how much of F is going to accelerate m1 and how much is going to accelerate m2. You can't do that with a free-body diagram in this case.
 

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